Abstract
This study provides a spatiotemporal characteristic analysis method based on multi-source data fusion and origin–destination (OD) deduction for the field of intelligent bus dispatching. First, it comprehensively considers the impact of data from the foundation layer, interaction layer, and output layer. Combining the Dempster–Shafer theory evidence method with Jensen–Shannon divergence to enhance fusion credibility can ensure the quality of collected data and the accuracy of its fusion. Second, based on multi-source data cross fusion, the critical value of travel time difference is used to solve the number of passengers boarding at each station, and the travel chain method and attraction method are used to solve the number of passengers disembarking at each station. Finally, based on OD information, K-means clustering analysis was used to analyze the characteristics of bus operating time. A spatial delay propagation analysis was conducted by combining the running time between stations, the stopping time at stations, and the waiting time at intersections. This study can optimize the OD attraction intensity and address the issue of low accuracy in cross-layer data fusion. At the same time, the study can comprehensively obtain spatiotemporal distribution characteristics and provide decision-making support for optimizing bus routes.
1 Introduction
Multi-source data fusion has become a cornerstone of intelligent transportation systems (ITSs), underpinning multi-agent decision-making and congestion mitigation across diverse transport scenarios (Kessler et al., 2021; Li M. et al., 2025; Zhu et al., 2026; Kashinath et al., 2021; Trinh et al., 2022; Song et al., 2019). These methods have also been extensively applied beyond public transportation, including highway traffic analysis (Zhang J. et al., 2024; Wang P. et al., 2019; Qu et al., 2024), maritime vessel trajectory prediction (Xiao et al., 2023; Chen S. et al., 2025), and multimodal urban mobility modeling (Dhanasekaran et al., 2024; Fang et al., 2021; 2022; Hu et al., 2024; Chen et al., 2024).
Despite the recognized value of multi-source data fusion in enhancing transit reliability and service quality (Lahat et al., 2015; Wang Y. et al., 2019; Li et al., 2024; Zhang H. et al., 2025), significant data integration challenges persist in reconciling heterogeneous formats, temporal misalignments, and conflicting evidence across basic and interaction layers. To address device dependency limitations, Rong et al. (2022) proposed the Du–Bus method for estimating real-time waiting times without GPS sensors, while Jiang et al. (2024) utilized kernel principal component analysis (PCA) to mitigate data dimensionality conflicts in driver-vehicle systems. These advancements underscore that overcoming integration barriers, particularly in aligning integrated circuit (IC) card records, GPS trajectories, and mobile payment logs, is a prerequisite for accurately inferring complex passenger behaviors and operational states.
Methodological innovations further demonstrate the adaptability of fusion techniques to urban transit contexts. Wang S. et al. (2019) alleviated data sparsity by extracting traffic event signals from social media and integrating them with GPS detection data, while Wang et al. (2025) analyzed three-dimensional factors, including road alignment, lighting environment, and traffic flow, through vehicle-road-person fusion in spiral tunnels. Liu et al. (2021) improved traffic speed estimation by merging floating car and microwave sensor data using a GA–PSO–BP neural network, and Zhang Y. et al. (2024) introduced a multi-view velocity aggregation algorithm for high-resolution urban traffic speed estimation. Wang Z. et al. (2024) and Lu et al. (2024) developed scenario-specific fusion models, while Wan and Gao (2025) emphasized the broad applicability of these approaches.
Despite these advances, two critical limitations remain in applying multi-source data fusion to public transportation OD analysis.
First, most studies rely heavily on limited data sources such as IC card or GPS data (Rong et al., 2022; Li et al., 2024), rarely incorporating bus operation statistics, city map data, and mobile payment data, which restricts the comprehensiveness of passenger flow characterization.
Second, existing fusion methods often struggle with missing values and overlapping interactions among heterogeneous sources, resulting in low recognition accuracy and difficulties in capturing spatiotemporal distribution characteristics of passenger flow and OD matrices (Zhang H. et al., 2025; Zhang S. et al., 2025; Wang Y. et al., 2024).
To address these gaps, this study partitions bus operation data into basic, interaction, and output layers, conducts feature-level and decision-level fusion, and optimizes OD attraction intensity through cross-checking and cross-fusion strategies.
2 Stage one: multi-source data integration
2.1 Multi-source data stratification
Multi-source data can be categorized into three layers: the foundational layer, the interaction layer, and the output layer (Shang et al., 2022).
The basic-layer information includes (1) bus stop information data, such as bus stop numbers, station names, and latitude and longitude of the station location; (2) Bus operation statistics data, including various operating schedules and mileage, driver scheduling, and vehicle turnover, as well as GPS data for individual routes; (3) City map data, which provide vehicle travel trajectories for constructing a route network during the traffic simulation process; and (4) APP data that can obtain specific information such as routes, stations, and license plate numbers. The interaction layer information includes (1) IC card data, (2) Mobile payment data that includes information on the proportion of bus travel modes and frequency of passenger travel, and (3) GPS data that provides delay information for vehicles. The output layer information includes (1) OD information derivation and (2) visualization analysis.
Due to the different granularity and dimensions of data information fusion in each layer, the basic layer is fused at the data and feature levels. In contrast, the interaction layer is fused at the feature and decision levels. This study optimizes the OD attraction intensity and improves its accuracy by cross-fusing multi-source data. The logical relationship of cross fusion is shown in Figure 1.
FIGURE 1
2.2 Data fusion methods in the interaction layer
The basic-layer information consists of raw, heterogeneous, and temporally tagged records collected directly from urban public transport subsystems, such as IC cards, GPS, and dispatch schedules, that retain high interpretability but often suffer from incompleteness and semantic inconsistency. These characteristics render classical probabilistic models less suitable, as they typically require complete prior distributions and error-free observations. In contrast, Dempster–Shafer (D–S) evidence theory is inherently well-suited to this context: it allows each basic-layer dataset to be treated as an independent body of evidence, supports the fusion of heterogeneous inputs without relying on strict prior probabilities, and quantifies the uncertainty of inferred OD pairs through belief and plausibility intervals, thereby providing a robust mechanism to upgrade partial basic-layer data into reliable passenger flow insights.
The application of D–S theory in this study relies on three fundamental assumptions. First, it assumes a finite frame of discernment, meaning there is a finite set of all possible and mutually exclusive hypotheses regarding passenger travel states (e.g., candidate origin–destination pairs). Second, it assumes direct evidential support: each basic-layer data source (IC card, GPS, and mobile payment) provides a degree of support to these hypotheses, ranging from 0 to 1, without requiring a complete prior probability distribution. Third, it assumes independent evidence combination, in which the conflict or agreement between different data sources is mathematically resolved to derive a fused belief.
To measure the similarity between probability distributions derived from these heterogeneous sources, the Jensen–Shannon (J–S) divergence is adopted instead of alternatives such as the Kullback–Leibler divergence. This choice is justified by its superior properties for public transit data: unlike the Kullback–Leibler divergence, the J–S divergence is symmetric, always yields a finite value even when comparing distributions with non-overlapping supports (common in sparse IC card or GPS data), and provides a bounded measure of dissimilarity. This makes it particularly effective for evaluating the consistency of evidence before fusion (Endres and Schindelin, 2003).
Based on the basic-layer information, the interaction layer information can obtain passenger OD information. Based on the D–S theory method, information weights are obtained by combining information entropy and the J–S divergence matrix, thereby facilitating data fusion. As a standard metric, the J–S divergence is mathematically bounded and inherently stable for the non-identical distributions derived from sparse transit data, requiring no iterative boundary adjustments. The fusion process of multi-source data is as follows:
The three basic information allocation functions BPA1, BPA2, and BPA3 (referred to as mass functions) are formed by collecting IC card data, mobile payment data, and GPS data from the station departure paths.
represents an event of uncertain information , represents an element, is a mass function, and represents a set of sample spaces. The information entropy of each type of information is calculated:
3. The difference in three types of information is calculated:
Here,
represents three types of random information, and
represents a power function.
4. The calculation method of each element in the difference measurement matrix of three types of information:
5. The evidence difference (ED) between each piece of information is calculated based on the difference measurement matrix:
6. represents the divergence calculation method as follows:
Here,
, and
;
and
represent two probability distribution forms of random variables.
7. The average divergence of various types of information is calculated:
8. Based on the average divergence , the credibility of various types of information is calculated as follows:
9. The three types of information are optimized based on credibility and the difference information (DI) is calculated:
10. The three types of information are normalized to obtain their respective weights :
11. Taking a fixed vehicle within a unit time granularity as an example, it is known that the number of boarding stops collected from various types of information is . Combining the D–S combination rule to fuse the travel paths of three types of information, the actual number of boarding stops obtained is :
3 Stage two: OD information deduction methods
Based on the actual number of bus stops , the number of passengers boarding at the origin is determined using the critical value of travel time differences. The number of passengers alighting at the destination is determined using the travel chain and the attraction method (Zhao et al., 2024; Respati et al., 2023).
3.1 Solving using the threshold of travel time difference
The threshold for the difference in boarding times is defined as follows: when the difference between two boarding times exceeds this threshold, it indicates that the corresponding boarding stations are different. The opposite is also true. The determination and selection of this threshold directly affect the identification of passengers’ boarding stations.
The total number of boardings is composed of two forms: the number of IC card swipes and the number of rides paid via mobile payment. Payment times vary, and there are both duplicates and missing records. The number of stations traveled using an IC card is recorded as
, and the number of stations traveled using mobile payment is recorded as
. After cross-referencing, making decisions, and integrating various types of data, the actual total number of bus stop stations is
. Therefore, the critical value of the travel time difference
is determined by comparing
and
. It is specifically divided into seven steps:
The travel times are arranged in order from morning to evening, and the time difference between passengers boarding in consecutive trips is calculated; then, the differences are sorted in ascending order.
The actual number of bus stops where passengers get on is determined, and the smallest difference in travel time is initially selected as the critical value .
If the time difference between two adjacent passengers swiping their IC cards is , it can be determined that they boarded at the same station, and the station is recorded as . All boarding stations are recorded in order; the total number of stations at which the IC card was tapped is
4. The time difference between two consecutive passengers swiping their IC cards is recorded as . indicates that they boarded at different stations; indicates that there is another mode of travel. [·] indicates rounding to the nearest whole number. The number of stations passed between two adjacent passengers boarding at different stations is
The total number of stations is
5. The total number of boarding stops is
6. refers to the actual number of stops at which the vehicle stops. indicates that the selected value is too small, and a larger value should be chosen.
7. If , the critical value of the selected travel time difference is determined.
3.2 Calculation of the number of passengers boarding at each station
After determining
, the boarding station
and the number of passengers boarding at each station
are determined. Here, the boarding record corresponding to station
is
, the passenger arrival time is recorded as
, the vehicle’s passenger capacity is
, and the number of passengers getting off is
. The travel records are sorted by time and calculated as follows:
The time difference between two consecutive ride records is
2. When , it is determined that both passengers board at the same station. The corresponding station is recorded as , and the number of passengers boarding is
3. When , both passengers board at different stations. At this time, the corresponding station is recorded as , and the number of passengers boarding is
The calculation of passenger boarding numbers is derived from IC card and mobile payment records, with data integrity verified through cross-referencing with GPS dispatch logs to ensure consistency.
3.3 Calculation of the number of disembarking passengers at the station
The number of passengers getting off at each station is derived by integrating the travel chain method and the station attraction method (Cai et al., 2025; Li et al., 2022). This study establishes a set through the following four scenarios, assuming the following:
Assumption 1When the bus travel chain is closed, the stops for passengers to get on and off the bus coincide.
Assumption 2When the travel chain shows a slight closure, the next boarding station for passengers appears near the downstream station of the route.
Assumption 3When Assumptions 1 and 2 are not met, the passenger’s exit point is generally a recent multiple boarding station, and the passenger’s exit attraction rate is positively correlated with the number of boarding times.
Assumption 4When the recent collection of boarding stations cannot be obtained, it is assumed that passengers will disembark at downstream stations, and the probability of disembarking is proportional to the passenger flow at the station.
For the convenience of model construction, suppose a passenger boards a bus at station and takes bus route to depart in the downstream direction. Based on this, the following four sets are established.
Set represents a collection of bus stops located downstream of the station, forming a closed travel chain. Set represents a collection of nearby bus stops located within 100 m of the set, forming a micro closed travel chain. Set : Select a recent period and group the boarding stations into a set of multiple boarding stations, and the number of boarding times at each station in this set should be greater than a certain value. Set : For downstream sites with high passenger traffic, the passenger traffic value of the site set should be greater than a certain value.
Based on the above four hypothetical scenarios, the probability of getting off is directly proportional to the passenger capacity of the vehicle . The number of passengers getting off at station is represented as :
Assuming that the passenger’s boarding station is
, the probability of getting off
is divided into the following three situations:
If the station satisfies , and the travel chain is in a closed state, the probability of getting off at the station is as follows:
2. If the station meets , its travel chain is in a slightly closed state. If the nearby station is station , the probability of getting off is as follows:
3. If the station meets , it is necessary to analyze the probability of getting off from the aggregate level. The probability of getting off is as follows:
In the formula, represents the number of times the train stops at the station , represents the number of sites in the set , and represents a random site.
4 Stage three: visualization analysis for spatiotemporal distribution characteristics
4.1 Analysis of time characteristics based on the K-means clustering analysis
Based on the basic layer of bus operation data in stage one, the time distribution of vehicles at each station is obtained (
Xu et al., 2021). The K-means method is used to divide the operating periods and perform cluster analysis, as follows:
Step 1: samples are randomly selected (Sinaga and Yang, 2020) from the sample as the center vector.
Step 2: The distance between each sample point and the center vector is the Euclidean distance, and the minimum value is calculated and taken as the clustering center for that sample point.
Step 3: The center clusters are continuously updated, and the mean of the sample points obtained from the previous iteration is used as a vector.
Step 4: During the clustering process, determine whether the clustering centers of each sample point have changed. If they have changed, return to step 2 and continue updating until the results are displayed.
4.2 Delay propagation in the spatial communication characteristics
The spatial characteristics of bus operation delay are related to the running time between stations, the stopping time at stations, and the waiting time at intersections. According to the fusion of the interaction layer in stage one, the number of passengers boarding and disembarking at the same station can be obtained as
and
, respectively. The calculation process is as follows:
The running time between stations
In the formula,
represents the passenger capacity of the vehicle at station
;
represents the running time of the inter-station (s);
represents the departure time of the vehicle at station
;
represents the arrival time of the vehicle at station
; and
represents the number of sites.
2. The stopping time at stations
In the formula,
represents the number of passengers boarding at station
;
represents the number of passengers getting off at station
;
represents the average boarding and alighting time per passenger (s);
represents the boarding and alighting time of passengers at station
; and
is the average time for buses to open and close doors, as well as to accelerate and decelerate when entering and exiting the station.
3. The waiting time at intersections
Here, represents the average remaining red light waiting time for vehicles to arrive at intersection ; represents the number of intersections.
5 Case study
5.1 Classification of Ganzhou bus data and OD deduction
The foundational data for this study originate from the operational records of the bus Route K
2in Ganzhou during June 2022. The number of sites
is 12. The number of intersections
is 4. The average waiting time
for vehicles to arrive at intersection
is 5 s. The average time
for each passenger to get on and off the bus is 2 s. The average acceleration and deceleration time
for buses is 30 s. In K-means clustering analysis, a random sample size of
is 100. The departure and arrival times of vehicles are obtained from operational statistical data. The main information is as follows:
City smart card system data
The Ganzhou smart card system includes IC card ride data and mobile payment receipts. Tables 1 and 2 show partial data of the daily settlement report for IC cards and mobile payments on 6 June 2022.
TABLE 1
| Vehicle mounted device number | Driver ID | Route number | Operating hours | Issuing card number | Unit price | Balance | Transaction type | Physical card number |
|---|---|---|---|---|---|---|---|---|
| 1528 | 4263 | 100100310 | 2022-6-6 17:03 | 1036933 | 1 | 1 | 13 | 0036E484 |
| 1528 | 4263 | 100100310 | 2022-6-6 8:52 | 1118434 | 1 | 11 | 13 | B823F082 |
| 1528 | 4263 | 100100310 | 2022-6-6 9:51 | 1077389 | 1 | 166 | 13 | 67B9503D |
| 1528 | 4263 | 100100310 | 2022-6-6 19:22 | 1082449 | 1 | 1 | 13 | 4CA0A43C |
| 1528 | 4263 | 100100310 | 2022-6-6 19:22 | 1082449 | 1 | 0 | 13 | 4CA0A43C |
| 1528 | 4263 | 100100310 | 2022-6-6 19:30 | 1017924 | 1 | 42 | 13 | B3F11CE6 |
| 1528 | 4263 | 100100310 | 2022-6-6 19:30 | 1017924 | 1 | 41 | 13 | B3F11CE6 |
| 1528 | 4263 | 100100310 | 2022-6-6 19:30 | 1017924 | 1 | 40 | 13 | B3F11CE6 |
Partial data of bus IC card.
TABLE 2
| SIM | Vehicle mounted device number | Transaction type | Collection time | Deduction | Route number |
|---|---|---|---|---|---|
| _ | 1528 | 10 | 2022-6-6 17:10 | 1 | 100100310 |
| _ | 1528 | 12 | 2022-6-6 8:50 | 1 | 100100310 |
| _ | 1528 | 12 | 2022-6-6 9:55 | 2 | 100100310 |
| _ | 1528 | 12 | 2022-6-6 19:15 | 1 | 100100310 |
| _ | 1528 | 10 | 2022-6-6 19:18 | 1 | 100100310 |
| _ | 1528 | 10 | 2022-6-6 19:27 | 2 | 100100310 |
| _ | 1528 | 11 | 2022-6-6 19:19 | 1 | 100100310 |
| _ | 1528 | 11 | 2022-6-6 19:40 | 1 | 100100310 |
Partial mobile payment data for buses.
The research mainly utilizes the mapping relationship between user card number, car phone number, and payment form in mobile payment data to obtain ride information. The mobile payment data in Ganzhou is stored as CSV files (with some data encrypted).
Table 3shows partial GPS data of buses in Ganzhou on 6 June 2022. The data are saved in CSV format, and the sampling interval varies due to differences in data collection equipment. The GPS data comprise the following data segments:
2. Bus stop information data
TABLE 3
| Vehicle | Record time | Longitude | Latitude | Speed (m/s) | Direction | Validity |
|---|---|---|---|---|---|---|
| 05180D | 2022-6-6 20:34 | 113.1264 | 22.9802 | 5 | 140 | 1 |
| 05180D | 2022-6-6 20:36 | 113.126 | 22.98052 | 12 | 60 | 1 |
| 05180D | 2022-6-6 20:39 | 113.1253 | 22.9803 | 12 | 70 | 1 |
| 05180D | 2022-6-6 20:40 | 113.1246 | 22.9803 | 11 | 70 | 1 |
| 05180D | 2022-6-6 20:43 | 113.1241 | 22.98008 | 7 | 80 | 1 |
Partial GPS data of buses.
The information data of public transportation stations in Ganzhou is shown in
Table 4, including station numbers, station names, latitude and longitude of station locations, route names, and platform forms, totaling 1441 pieces of information.
3. Bus operation statistics data
TABLE 4
| Site number | Station | Longitude | Latitude | Line | Platform |
|---|---|---|---|---|---|
| 10010012 | Dukou Road | 114.953142 | 25.85306 | 7 | Harbor style |
| 10010014 | Dukou Road | 114.953513 | 25.852832 | | Harbor style |
| 10010020 | Jiafu International Community | 114.960104 | 25.852638 | 7 | Harbor style |
| 10010022 | Jiafu International Community | 114.959311 | 25.853073 | | Harbor style |
| 10010024 | Nanyang Dongsheng Community | 114.955896 | 25.853021 | 7 | Harbor style |
| 10010032 | Nanyang Dongsheng Community | 114.956133 | 25.852898 | | Harbor style |
| 10010034 | Dukou Road East | 114.964761 | 25.851699 | 7 | Harbor style |
| 10010042 | Dukou Road East | 114.9648 | 25.851267 | | Harbor style |
Partial data of bus stop information.
The statistics of bus operation and production are shown in Table 5, including line vehicle numbers, schedules, regular mileage, passenger mileage, non-operating mileage, operating mileage, etc.
TABLE 5
| Vehicle | Planned shift | Complete shift | Regular mileage /km | Passenger mileage /km | Non-operational mileage /km | Operating mileage /km |
|---|---|---|---|---|---|---|
| 00113D | 39 | 38 | 744.8 | 744.8 | 4.3 | 749.1 |
| 00779D | 67 | 67 | 1313.2 | 1313.2 | 0 | 1313.2 |
| 01160D | 67 | 67 | 1313.2 | 1313.2 | 10.4 | 1323.59 |
| 01655D | 67 | 67 | 1313.2 | 1313.2 | 0 | 1313.2 |
| 02386D | 67 | 59 | 1156.4 | 1156.4 | 0 | 1156.4 |
| 04699D | 69 | 53 | 1038.8 | 1038.8 | 7.56 | 1046.36 |
| 05180D | 68 | 53 | 1038.8 | 1038.8 | 0 | 1038.8 |
| 08846D | 70 | 65 | 1274 | 1274 | 0 | 1274 |
Partial data of K2 line operation statistics from June 2022.
It is convenient to analyze the driver’s scheduling and vehicle turnover situation, as well as extract GPS data for individual routes, using the operation and production statistics table.
Rigorous preprocessing was applied to the basic-layer data to eliminate redundancy and noise prior to fusion. Duplicate records and GPS outliers, identified via speed thresholds (>80 km/h) and missing key fields, were removed, while missing dispatch entries were forward-filled to ensure logical consistency (Si et al., 2023). This cleaning ensures that the retained observations constitute reliable evidence for the Dempster–Shafer (D–S) framework, allowing the construction of high-quality basic probability assignments (BPAs) essential for accurate passenger OD inference (Rahmani et al., 2015).
During the research period, the proportion of passengers using card swiping for travel was relatively high. The arrival rate of passengers followed a Poisson distribution, which can represent the characteristics of the OD travel chain. Therefore, based on Formulas 1–23, the station spacing and passenger OD distribution during the study period were obtained. The distance matrix between 12 stations is shown in Table 6. According to the integration of the interaction layer in stage one, the number of passengers boarding and alighting at the same station can be obtained. For example, the boarding and alighting situations of each of 10 randomly selected vehicles from the time period of 8:00–9:00 are shown in Table 7.
TABLE 6
| Station | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | S11 | S12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| S1 | — | 199 | 236 | 534 | 864 | 1062 | 1319 | 2180 | 3020 | 3452 | 4426 | 5520 |
| S2 | — | — | 117 | 415 | 745 | 943 | 1200 | 2061 | 2901 | 3333 | 4307 | 5401 |
| S3 | — | — | — | 298 | 628 | 826 | 1083 | 1944 | 2784 | 3216 | 4190 | 5284 |
| S4 | — | — | — | — | 330 | 528 | 785 | 1646 | 2486 | 2918 | 3892 | 4986 |
| S5 | — | — | — | — | — | 198 | 455 | 1316 | 2156 | 2488 | 3562 | 4656 |
| S6 | — | — | — | — | — | — | 257 | 1118 | 1958 | 2390 | 3364 | 4458 |
| S7 | — | — | — | — | — | — | — | 861 | 1701 | 2133 | 3107 | 4201 |
| S8 | — | — | — | — | — | — | — | — | 840 | 1272 | 2246 | 3340 |
| S9 | — | — | — | — | — | — | — | — | — | 432 | 1406 | 2500 |
| S10 | — | — | — | — | — | — | — | — | — | — | 974 | 2068 |
| S11 | — | — | — | — | — | — | — | — | — | — | — | 1094 |
| S12 | — | — | — | — | — | — | — | — | — | — | — | — |
Distance between stations (m).
TABLE 7
| Number of people | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | S11 | S12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| V1 (get on) | 7 | 1 | 10 | 3 | 8 | 2 | 8 | 8 | 1 | 9 | 10 | 0 |
| V1 (get off) | 0 | 0 | 9 | 0 | 5 | 0 | 7 | 5 | 0 | 5 | 3 | - |
| V2 (get on) | 8 | 7 | 2 | 12 | 1 | 5 | 12 | 3 | 5 | 7 | 6 | 0 |
| V2 (get off) | 0 | 5 | 0 | 5 | 0 | 6 | 2 | 0 | 3 | 1 | 2 | - |
| V3 (get on) | 11 | 1 | 12 | 8 | 12 | 5 | 1 | 12 | 2 | 8 | 9 | 0 |
| V3 (get off) | 0 | 0 | 5 | 4 | 7 | 0 | 0 | 6 | 0 | 2 | 3 | - |
| V4 (get on) | 9 | 7 | 6 | 8 | 5 | 15 | 8 | 2 | 10 | 1 | 10 | 0 |
| V4 (get off) | 0 | 5 | 3 | 6 | 0 | 10 | 7 | 0 | 9 | 0 | 0 | - |
| V5 (get on) | 5 | 3 | 7 | 1 | 13 | 10 | 10 | 9 | 3 | 6 | 7 | 0 |
| V5 (get off) | 0 | 0 | 3 | 0 | 5 | 5 | 3 | 6 | 0 | 2 | 3 | - |
| V6 (get on) | 8 | 1 | 9 | 8 | 10 | 7 | 8 | 1 | 7 | 6 | 9 | 0 |
| V6 (get off) | 0 | 0 | 2 | 3 | 2 | 3 | 4 | 0 | 3 | 2 | 2 | - |
| V7 (get on) | 13 | 5 | 7 | 9 | 12 | 1 | 8 | 7 | 9 | 2 | 13 | 0 |
| V7 (get off) | 0 | 2 | 3 | 1 | 3 | 0 | 3 | 5 | 5 | 12 | 8 | - |
| V8 (get on) | 10 | 9 | 9 | 1 | 10 | 6 | 9 | 1 | 8 | 5 | 8 | 0 |
| V8 (get off) | 0 | 5 | 3 | 0 | 2 | 4 | 5 | 0 | 3 | 3 | 2 | - |
| V9 (get on) | 8 | 7 | 1 | 9 | 8 | 10 | 9 | 7 | 8 | 1 | 6 | 0 |
| V9 (get off) | 0 | 3 | 0 | 5 | 2 | 6 | 3 | 1 | 2 | 0 | 2 | - |
| V10 (get on) | 12 | 8 | 15 | 10 | 12 | 7 | 12 | 11 | 9 | 7 | 8 | 0 |
| V10 (get off) | 0 | 5 | 6 | 3 | 9 | 5 | 6 | 7 | 12 | 2 | 3 | - |
Number of people getting on and off at each station.
5.2 Visual analysis of Ganzhou bus spatiotemporal distribution
5.2.1 Temporal distribution
Based on the basic-layer information, the regularity of bus travel time periods is explored. The operating time data of the K2 Road in Ganzhou City on 6 June 2022 were selected. It can be clearly seen that there are two distinct peaks in a day, namely, 7:28–9:25 and 16:34–18:20, which conform to the operating rules of the morning and evening peak periods on weekdays, as shown in Figure 2.
FIGURE 2
The delay times of each bus trip on the K2 route from June 2022 to December 2022 are evenly distributed, as shown in Figure 3. Selecting the delay time of each station on Monday, June 2022, through the standard deviation analysis in Figure 4, it can be seen that the delay time of each trip is around 1500 s.
FIGURE 3
FIGURE 4
The data of the K2 Road in Ganzhou on Monday, 6 June, and Friday, 10 June, are selected as the sample set. The sample clustering centers were obtained using the K-means clustering algorithm. A scatter plot of the time period division of buses throughout the day is drawn, with six colors representing clustering categories. Based on the travel habits of passengers, the bus schedule is divided into six time periods, as shown in Figure 5.
FIGURE 5
Category 1 corresponds to the morning rush hour, with a specific time range of 6:30–9:15.
Category 2 represents the off-peak period in the morning after the morning rush hour, with a specific time range of 9:15–11:20.
Category 3 represents entering the midday off-peak period, with a specific time range of 11:20–14:28.
Category 4 represents entering the afternoon off-peak period, with a time range of 14:28–16:16.
Category 5 corresponds to the evening rush hour, with a specific time range of 16:16–19:20.
Category 6 represents the low peak period in the evening after the evening rush hour, with a specific time range of 19:20–22:30.
The clustering analysis results highlight the clustering effect of traffic flow on weekdays. Traffic volume at different time periods affects the duration of bus operation, providing a direct basis for dispatchers to adjust bus headways during peak and off-peak periods.
5.2.2 Spatial communication
Buses exhibit spatial correlation during their operation at stops, intersections, and road sections. This visualization analysis is based on OD information and combined with
Formulas 24–
29for K
2in Ganzhou on 6 June 2022.
The running time between stations
As shown in
Figure 6, the travel time profiles for the upstream (Railway Station–Ganjiangyuan Ave. East) and downstream (Ganjiangyuan Ave. East–Wulong Bridge) segments exhibit similar trends. Crucially, the high-fidelity OD data derived from multi-source fusion allow for the precise quantification of the correlated volatility between these segments, enabling operators to distinguish between systemic network delays and localized disturbances for targeted headway adjustments.
2. The stopping time at stations
FIGURE 6
As shown in
Figure 7, the dwell time at Ganjiangyuan Avenue East correlates closely with that at the Railway Station. Leveraging the fused OD data, this study quantifies this inter-station coupling effect, allowing operators to predict downstream dwell delays based on upstream conditions and optimize schedule recovery strategies.
3. The waiting time at intersections
FIGURE 7
As illustrated in Figure 8, the travel time curves between the Telecom Building and Dongyangshan Strong Department Store exhibit a smooth trajectory, whereas the segment between Dongyangshan Road and the Municipal Administrative Service Center shows significant fluctuations due to an intermediate intersection. Crucially, because the OD data are derived from the proposed multi-source fusion framework, we can precisely quantify the stationary delay component induced by the signal cycle rather than merely observing the fluctuation. For transit operators, this means the fusion output provides actionable intelligence: dispatchers can identify whether a bus is delayed due to network congestion (requiring schedule recovery) or held at a signal (requiring headway regulation), thereby optimizing real-time control strategies based on accurate delay attribution.
FIGURE 8
6 Conclusion
The innovation of this research is reflected in the following.
Optimized fusion mechanism: Information entropy is introduced to dynamically weight interaction-layer evidence, while J–S divergence ensures robust consistency between fused distributions, resolving redundancy and conflict in raw data.
High-fidelity OD inference: A travel time difference threshold is established to accurately resolve boarding numbers at stops, complemented by travel chain and attraction methods, to refine OD matrix precision.
Spatiotemporal operational insights: Beyond visualization, the derived OD data enable quantitative spatiotemporal attribution. Spatially, the method decomposes intersection-induced delays and quantifies inter-station coupling effects. Temporally, it identifies clustered traffic periods to guide dynamic headway adjustments.
Future work will extend this feasibility study by (1) integrating GIS to visualize network-wide spatial desire lines, overcoming the limitations of static tabular outputs; (2) conducting quantitative baseline comparisons against conventional fusion models and performing statistical significance tests; and (3) refining the threshold calibration and mathematical objective functions to accommodate broader operational scenarios.
Statements
Data availability statement
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
Author contributions
JX: Software, Validation, Investigation, Visualization, Formal analysis, Methodology, Writing – original draft. JM: Validation, Funding acquisition, Writing – review and editing, Methodology, Supervision. ML: Validation, Data curation, Writing – review and editing, Supervision, Conceptualization.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the National Natural Science Foundation of China under Grant (No.52302375).
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
Publisher’s note
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Summary
Keywords
fusion credibility, intelligent bus dispatching, multi-source data fusion, origin–destination deduction, spatiotemporal distribution
Citation
Xi J, Ma J and Lei M (2026) Mining of bus spatiotemporal distribution based on multi-source data fusion and OD deduction. Front. Future Transp. 7:1875006. doi: 10.3389/ffutr.2026.1875006
Received
07 May 2026
Revised
22 June 2026
Accepted
01 July 2026
Published
29 July 2026
Volume
7 - 2026
Edited by
Mehrdad Dianati, Queen’s University Belfast, United Kingdom
Reviewed by
Alfa Narendra, Universitas Negeri Semarang, Indonesia
Xiao Li, Shanghai Jiao Tong University, China
Updates
Copyright
© 2026 Xi, Ma and Lei.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Jie Ma, majie9001@nuaa.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.